-x^2+33x-252=0

Solution for -x^2+33x-252=0 equation:

-x^2+33x-252=0

We add all the numbers together, and all the variables

-1x^2+33x-252=0

a = -1; b = 33; c = -252;
Δ = b2-4ac
Δ = 332-4·(-1)·(-252)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-9}{2*-1}=\frac{-42}{-2}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+9}{2*-1}=\frac{-24}{-2}
=+12
$